Question

A firm produces a product in a competitive industry and has a total cost function (TC) of TC(a) 60+4q+2q2 and a marginal cost function (MC) of MC(q) = 4 + 4q. At the given market price (P) of $20, the firm is producing 4.00 units of output. Is the firm maximizing profit?V What quantity of output should the firm produce in the long run? The firm should produce unit(s) of output. (Enter your response as an integer.)

Answer 1

A firm in perfectly competitive market maximizes profit by producing at the point where price = MC.

Therefore, setting 4 + 4q = 20

Or, 4q = 16

Or, q = 4

This firm's profit maximizing output is 4 units. Therefore, the firm is maximizing profit.

In the long run, a perfectly competitive firm produces on the minimum point on ATC so that it earns zero economic profit in long run.

ATC = (TC/q) = (60/q) +4 + 2q

If ATC is minimized then d(ATC)/dq = 0

Or, -(60/q^{​​​​​​2}​​​​​) + 0 + 2 = 0

Or, (60/q^{​​​​​​2}) = 2

Or, q^{​​​​​​2}​ = 30

Or, q = √30 = 5.48 = 6 units of output